Long-time Brownian dynamics of hard and sticky colloids by geometric projection
Abstract
Particle-resolved colloid simulations are often limited by the fastest microscopic time scale retained in the model, which can be many orders of magnitude shorter than the collective process of interest. This is especially restrictive for aggregating colloids, where explicit near-contact potentials force the time integration to resolve the rapid positional relaxation of bonded pairs within narrow attractive wells. Here we introduce an overdamped constraint-based Brownian dynamics method that replaces the time-resolved integration of stiff near-contact forces by a geometric projection step. After each free Brownian update, hard-sphere exclusion, sticky bonds, and hard-wall interactions are enforced by projecting the particle positions onto the constrained configuration set. The method preserves hard-sphere structure and diffusion, recovers the aggregation kinetics of sticky hard spheres, and extends the physical time reached at fixed computational cost by one to two orders of magnitude relative to the explicit-potential simulations tested here. This acceleration makes Brownian-dominated, low-Péclet electrophoretic deposition accessible to particle-scale simulations, revealing a pathway in which the suspension first densifies and only subsequently develops a bonded network. Implemented as a LAMMPS fix, the framework provides a modular route to long-time Brownian simulations of dense constrained colloidal systems.
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BibTeX
@misc{martin2026longtime,
title = {{Long-time Brownian dynamics of hard and sticky colloids by geometric projection}},
author = {Rémi Martin and Sandrine Duluard and Céline Merlet},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05018},
eprint = {2611.05018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05018},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-time Brownian dynamics of hard and sticky colloids by geometric projection
AU - Rémi Martin
AU - Sandrine Duluard
AU - Céline Merlet
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05018
UR - https://arxiv.org/abs/2611.05018
AB - Particle-resolved colloid simulations are often limited by the fastest microscopic time scale retained in the model, which can be many orders of magnitude shorter than the collective process of interest. This is especially restrictive for aggregating colloids, where explicit near-contact potentials force the time integration to resolve the rapid positional relaxation of bonded pairs within narrow attractive wells. Here we introduce an overdamped constraint-based Brownian dynamics method that replaces the time-resolved integration of stiff near-contact forces by a geometric projection step. After each free Brownian update, hard-sphere exclusion, sticky bonds, and hard-wall interactions are enforced by projecting the particle positions onto the constrained configuration set. The method preserves hard-sphere structure and diffusion, recovers the aggregation kinetics of sticky hard spheres, and extends the physical time reached at fixed computational cost by one to two orders of magnitude relative to the explicit-potential simulations tested here. This acceleration makes Brownian-dominated, low-Péclet electrophoretic deposition accessible to particle-scale simulations, revealing a pathway in which the suspension first densifies and only subsequently develops a bonded network. Implemented as a LAMMPS fix, the framework provides a modular route to long-time Brownian simulations of dense constrained colloidal systems.
ER -